The Library · Mathematics

Mathematics
Pre-University

Grades 11–12 · A-Level, IB, JEE

FoundationLower SecondaryUpper SecondaryPre-UniversityUniversity Foundations

0 of 84 lectures are ready to read. The rest are listed so you can see where the subject goes; each one switches on as it is finished.

Pure Algebra and Functions

Polynomials0 of 5 ready
  1. 01Polynomial division — algebraic long divisioncoming soon
  2. 02The factor theorem — testing for factorscoming soon
  3. 03The remainder theorem — remainders without dividingcoming soon
  4. 04Solving cubic equations — factor theorem approachcoming soon
  5. 05Partial fractions — splitting rational expressionscoming soon
Exponentials and Logarithms0 of 5 ready
  1. 01Exponential functions — growth and decay graphscoming soon
  2. 02The natural exponential e to the x — why e is specialcoming soon
  3. 03Natural logarithm ln x — the inverse of e to the xcoming soon
  4. 04Modelling with exponentials — growth and decaycoming soon
  5. 05Logarithmic graphs — linearising exponential datacoming soon
Trigonometry Advanced0 of 9 ready
  1. 01Radians — a better way to measure anglescoming soon
  2. 02Exact values and the unit circlecoming soon
  3. 03Graphs of sin cos tan — full picturecoming soon
  4. 04Reciprocal trig functions — sec cosec cotcoming soon
  5. 05The trig identities — sin squared plus cos squared equals 1 and beyondcoming soon
  6. 06Compound angle formulaecoming soon
  7. 07Double angle formulae — special casescoming soon
  8. 08Solving trig equations — general solutionscoming soon
  9. 09The R sin theta plus alpha form — combining sin and coscoming soon
Coordinate Geometry and Parametrics0 of 4 ready
  1. 01The equation of a circle — centre and radius formcoming soon
  2. 02Tangents and normals to a circlecoming soon
  3. 03Parametric equations — a different way to describe curvescoming soon
  4. 04Cartesian and parametric — conversion practicecoming soon

Calculus

Differentiation0 of 8 ready
  1. 01Differentiation from first principles — the limit definitioncoming soon
  2. 02Differentiating polynomials — power rulecoming soon
  3. 03The chain rule — differentiating composite functionscoming soon
  4. 04The product rule — differentiating productscoming soon
  5. 05The quotient rule — differentiating fractionscoming soon
  6. 06Differentiating e to the x ln x sin x cos xcoming soon
  7. 07Implicit differentiation — when y isn't isolatedcoming soon
  8. 08Parametric differentiation — dy over dx from x t and y tcoming soon
Applications of Differentiation0 of 5 ready
  1. 01Stationary points — finding and classifyingcoming soon
  2. 02Increasing and decreasing functionscoming soon
  3. 03Optimisation — maximum and minimum problemscoming soon
  4. 04Rates of change — connected ratescoming soon
  5. 05Curve sketching — using calculuscoming soon
Integration0 of 6 ready
  1. 01Integration as anti-differentiation — the reversecoming soon
  2. 02Integrating standard functions — e to the x one over x sin coscoming soon
  3. 03The definite integral — area under a curvecoming soon
  4. 04Area between two curvescoming soon
  5. 05Integration by substitutioncoming soon
  6. 06Integration by parts — integral u dv equals uv minus integral v ducoming soon
Advanced Integration and Differential Equations0 of 5 ready
  1. 01Integrating partial fractions — splitting firstcoming soon
  2. 02Volumes of revolution — rotating curvescoming soon
  3. 03Differential equations — separating variablescoming soon
  4. 04First-order linear DEs — the integrating factorcoming soon
  5. 05Modelling with differential equationscoming soon

Pure Topics

Sequences Series and Binomial0 of 6 ready
  1. 01Arithmetic sequences — finding the nth termcoming soon
  2. 02Sum of an arithmetic seriescoming soon
  3. 03Geometric sequences — the common ratiocoming soon
  4. 04Sum of a geometric series — finite and infinitecoming soon
  5. 05The binomial theorem — expanding 1 plus x to the ncoming soon
  6. 06Maclaurin series — approximating functionscoming soon
Proof0 of 4 ready
  1. 01Proof by deduction — building logical argumentscoming soon
  2. 02Proof by contradiction — assuming the oppositecoming soon
  3. 03Proof by induction — the domino argumentcoming soon
  4. 04Disproof by counter-examplecoming soon
Complex Numbers0 of 6 ready
  1. 01What is a complex number — introducing i equals root minus 1coming soon
  2. 02Arithmetic with complex numbers — add subtract multiplycoming soon
  3. 03The complex conjugate and dividing complex numberscoming soon
  4. 04The Argand diagram — complex numbers as pointscoming soon
  5. 05Modulus-argument form — r cos theta plus i sin thetacoming soon
  6. 06De Moivre's theorem and applicationscoming soon

Mechanics

Kinematics with Calculus0 of 3 ready
  1. 01Displacement velocity acceleration as vectorscoming soon
  2. 02Using calculus in kinematics — integrate and differentiatecoming soon
  3. 03Kinematics problems using calculuscoming soon
Forces and Newton's Laws0 of 4 ready
  1. 01Resolving forces — splitting into componentscoming soon
  2. 02Newton's second law as F equals ma vectorcoming soon
  3. 03Friction — the model and its limitscoming soon
  4. 04Moments — turning effect of a forcecoming soon
Statics and Moments0 of 3 ready
  1. 01Equilibrium of a rigid body — moments and forcescoming soon
  2. 02Centre of mass — where gravity actscoming soon
  3. 03Tilting and toppling conditionscoming soon

Statistics

Probability Distributions0 of 4 ready
  1. 01The binomial distribution — X tilde B n pcoming soon
  2. 02The normal distribution — shape and propertiescoming soon
  3. 03Standardising — using the Z tablecoming soon
  4. 04Normal approximation to the binomialcoming soon
Hypothesis Testing0 of 4 ready
  1. 01What is a hypothesis test — the logiccoming soon
  2. 02Hypothesis testing with the binomial distributioncoming soon
  3. 03Hypothesis testing with the normal distributioncoming soon
  4. 04Type I and Type II errorscoming soon
Regression and Correlation0 of 3 ready
  1. 01Spearman's rank correlation coefficientcoming soon
  2. 02Linear regression — least squares linecoming soon
  3. 03Using regression for prediction — and its limitscoming soon